Using Factor Theorem, show that :

(x - 2) is a factor of x³ - 2x² - 9x + 18. Hence, factorise the expression x³ - 2x² - 9x + 18 completely.

Using Factor Theorem, show that :

(x + 5) is a factor of 2x³ + 5x² - 28x - 15. Hence, factorise the expression 2x³ + 5x² - 28x - 15 completely.

Using the remainder theorem, factorise each of the following completely :

2x³ + x² - 13x + 6

Using the remainder theorem, factorise each of the following completely :

3x³ + 2x² - 23x - 30